Skewness and kurtosis ppt

A power point presentation on Skewness and kurtosis, displaying essential knowledge on the same with it's types and graphs for visual representation.

1. University Institute of Science Master of Science (Data Science)  Skewness and Kurtosis

2. Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. 

3. Skewness  Skewness refers to a distortion or asymmetry that deviates from the symmetrical bell curve, or  normal distribution , in a set of data. If the curve is shifted to the left or to the right, it is said to be skewed. Skewness can be quantified as a representation of the extent to which a given distribution varies from a normal distribution. A normal distribution has a skew of zero

4. Types of skewness  Positive skewed or right-skewed   Negative skewed or left-skewed

5. Positive skewed or right-skewed  In which most values are clustered around the left tail of the distribution while the right tail of the distribution is longer.  In positively skewed, the mean of the data is greater than the median (a large number of data-pushed on the right-hand side). T he mean, median, and mode of the distribution are positive rather than negative or zero.

6. Negative skewed or left-skewed In which more values are concentrated on the right side (tail) of the distribution graph while the left tail of the distribution graph is longer. T he mean of the data is less than the median (a large number of data-pushed on the left-hand side). T he mean, median, and mode of the distribution are negative rather than positive or zero.

7. Calculate the skewness coefficient of the sample I t truly scales the value down to a limited range of  -1 to +1. If the skewness is between -0.5 & 0.5, the data are nearly symmetrical. If the skewness is between -1 & -0.5 (negative skewed) or between 0.5 & 1(positive skewed), the data are slightly skewed. If the skewness is lower than -1 (negative skewed) or greater than 1 (positive skewed), the data are extremely skewed.

8. Kurtosis Kurtosis is a statistical measure, whether the data is heavy-tailed or light-tailed in a normal distribution. Kurtosis tell us about the  peakdness or flaterness of the distribution. Kurtosis is basically statistical measure that helps to identify the data around the mean. Types of excess kurtosis Leptokurtic or heavy-tailed distribution (kurtosis more than normal distribution). Mesokurtic (kurtosis same as the normal distribution). Platykurtic or short-tailed distribution (kurtosis less than normal distribution).

9. Leptokurtic (kurtosis > 3) Leptokurtic is having very long and skinny tails, which means there are more chances of outliers. Positive values of kurtosis indicate that distribution is peaked and possesses thick tails. An extreme positive kurtosis indicates a distribution where more of the numbers are located in the tails of the distribution instead of around the mean. Platykurtic (kurtosis < 3) Platykurtic having a lower tail and stretched around center tails means most of the data points are present in high proximity with mean. A platykurtic distribution is flatter (less peaked) when compared with the normal distribution.

10. Mesokurtic (kurtosis = 3) Mesokurtic is the same as the normal distribution, which means kurtosis is near to 0. In mesokurtic, distributions are moderate in breadth, and curves are a medium peaked height.

11. References www.analyticsvidhya.com www.slideshare.com www.statisticalaid.com